{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "EheA5_j_cEwc"
      },
      "source": [
        "##### Copyright 2019 Google LLC.\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "YCriMWd-pRTP"
      },
      "outputs": [],
      "source": [
        "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "OvRwFTkqcp1e"
      },
      "source": [
        "# Optimization in TensorFlow Quant Finance (TFF)\n",
        "\n",
        "TensorFlow Finance has built-in library for unconstrained numerical optimization. This notebook shows how to use it.\n",
        "\n",
        "\u003ctable class=\"tfo-notebook-buttons\" align=\"left\"\u003e\n",
        "  \u003ctd\u003e\n",
        "    \u003ca target=\"_blank\" href=\"https://colab.research.google.com/github/google/tf-quant-finance/blob/master/tf_quant_finance/examples/jupyter_notebooks/Optimization.ipynb\"\u003e\u003cimg src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" /\u003eRun in Google Colab\u003c/a\u003e\n",
        "  \u003c/td\u003e\n",
        "  \u003ctd\u003e\n",
        "    \u003ca target=\"_blank\" href=\"https://github.com/google/tf-quant-finance/blob/master/tf_quant_finance/examples/jupyter_notebooks/Optimization.ipynb\"\u003e\u003cimg src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" /\u003eView source on GitHub\u003c/a\u003e\n",
        "  \u003c/td\u003e\n",
        "\u003c/table\u003e"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "colab_type": "code",
        "id": "uG8UAZXjeUhf",
        "colab": {}
      },
      "source": [
        "#@title Upgrade to TensorFlow 2.1+\n",
        "!pip install --upgrade tensorflow"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "cellView": "both",
        "colab": {},
        "colab_type": "code",
        "id": "uG8UAZXjeUhf"
      },
      "outputs": [],
      "source": [
        "#@title Install TF Quant Finance\n",
        "!pip install tf-quant-finance"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "xmqzltQrwcDt"
      },
      "outputs": [],
      "source": [
        "#@title Imports\n",
        "import tensorflow as tf\n",
        "import tensorflow_probability as tfp\n",
        "import numpy as np\n",
        "import functools\n",
        "import matplotlib.colors as colors\n",
        "\n",
        "import tf_quant_finance.math.optimizer as tff_optimizer\n",
        "\n",
        "from matplotlib import pyplot as plt\n",
        "from IPython.core.pylabtools import figsize\n",
        "\n",
        "tf.compat.v1.enable_eager_execution()\n",
        "figsize(12, 8)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "b6W_agvli48r"
      },
      "outputs": [],
      "source": [
        "# Decorator for automatic gradient evaluation.\n",
        "def make_val_and_grad_fn(value_fn):\n",
        "  @functools.wraps(value_fn)\n",
        "  def val_and_grad(x):\n",
        "    return tfp.math.value_and_gradient(value_fn, x)\n",
        "  return val_and_grad"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "C4aB6EXR4EA2"
      },
      "source": [
        "## Simple example"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "rQClbumcAOiP"
      },
      "source": [
        "Below is an example of optimizing a function in TensorFlow Finance."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "height": 51
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 215,
          "status": "ok",
          "timestamp": 1569251881915,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": -60
        },
        "id": "sNkbWqxl4Ciq",
        "outputId": "ba954200-3ddc-4e6b-ef09-a5f0c8058873"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Argmin: [1. 1.]\n",
            "Objective value at argmin: 2.9042834203951543e-18\n"
          ]
        }
      ],
      "source": [
        "# Define a function.\n",
        "@make_val_and_grad_fn\n",
        "def func(x):\n",
        "  return (1 - x[0])**2 + 100*(x[1]-x[0]**2)**2\n",
        "\n",
        "# Start point for optimization.\n",
        "start = tf.constant([0.0, 0.0], dtype=tf.float64)\n",
        "\n",
        "# Optimize\n",
        "result = tff_optimizer.conjugate_gradient_minimize(func, start)\n",
        "print(\"Argmin: %s\" % result.position.numpy())\n",
        "print(\"Objective value at argmin: %s\" % result.objective_value.numpy())\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "WszX0iUY6fOe"
      },
      "source": [
        "In this example we used the Conjugate Gradinet optimization algorithm to optimize a function $f$ of two variables, defined as\n",
        "\n",
        "$$f(x, y) = (1-x)^2 + 100(y-x^2)^2.$$\n",
        "\n",
        "This is the [Rosenbrock function](https://en.wikipedia.org/wiki/Rosenbrock_function) and it has single local minimum $f(1, 1) = 0$, which is also a global minimum.\n",
        "\n",
        "We had to supply two things to the algorithm:\n",
        "\n",
        "* Callable which given a point $\\mathbf{x}$ calculates objective value at the point $f(\\mathbf{x})$ and gradient at the point $\\nabla f(\\mathbf{x})$.\n",
        "\n",
        "* Initial position. Conjugate Gradient method is an iterative method, i.e. it builds a sequence of points approaching the minimum. It needs to know at which point to start. In our case it is the origin (0, 0). Algorithm also uses initial position to infer dimensionality of the function domain and dtype which will be used to do all calculations.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "azvXu2m38_fT"
      },
      "source": [
        "## Automatic differentiation\n",
        "\n",
        "In example below we didn't explicitly specify gradient of objective function. That's because TensorFlow supports automatic differentiation. If you define a differentiable function using only TensorFlow ops that support gradients, you will be able to calculate its derivative at any point automatically.\n",
        "\n",
        "We used decorator `make_val_and_grad_func` to make from function which evaluates $f(\\mathbb{x})$ function which evaluates pair $f(\\mathbb{x}), \\nabla f(\\mathbb{x}).$ This decorator was defined at the top of this notebook.\n",
        "\n",
        "In principle, we could explicitly specify gradient:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "height": 34
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 144,
          "status": "ok",
          "timestamp": 1569251886444,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": -60
        },
        "id": "p2snEteL8-q4",
        "outputId": "90bdfd2a-c926-43bc-93fe-347ff79f1671"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[1. 1.]\n"
          ]
        }
      ],
      "source": [
        "def func_and_grad(position):\n",
        "  x, y = position[0], position[1]\n",
        "  func = (1 - x)**2 + 100*(y-x**2)**2\n",
        "  grad = tf.stack([\n",
        "    2* (x-1) - 400*(y-x**2) * x,\n",
        "    200 * (y-x**2)               \n",
        "  ])\n",
        "  return func, grad\n",
        "\n",
        "result = tff_optimizer.conjugate_gradient_minimize(func_and_grad, start)\n",
        "print(result.position.numpy())"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "CHRT_FLJ_9Gl"
      },
      "source": [
        "But we recommend to always use automatic differentiation."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "I0VKZHNGpMrm"
      },
      "source": [
        "## Tolerance\n",
        "\n",
        "Conjugate Gradient algorithm stops if any of following conditions is satisifed:\n",
        "\n",
        "* Maximum number of iterations (specified by parameter `max_iterations`) is reached;\n",
        "* Norm of gradient is not greater than `tolerance`. Note that norm is inf-norm, i.e. maximal absolute value over all coordinates of gradient;\n",
        "* Relative difference between values of objective function on $i$-th and $(i+1)$-th iterations is not greater than `f_relative_tolerance`;\n",
        "* Inf-norm between positions on $i$-th and $(i+1)$-th iterations is not greater than `x_tolerance`.\n",
        "\n",
        "Parameters `max_iterations`, `tolerance`, `f_relative_tolerance` and `x_tolerance` are parameters of optimization algorithm.\n",
        "By default `x_tolerance` and `f_relative_tolerance` are set to 0.\n",
        "\n",
        "Gradient tolerance is an important parameter. If it is too small, algorithm may perform many iterations in the neigborhood of the local minimum but never stop. If it is too big, algorithm may terminate too far from the minimum. Default value is $10^{-8}$.\n",
        "\n",
        "Example below shows how number of iterations and number of objective evaluations needed for optimization to converge depend on gradient tolerance. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "height": 525
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 12091,
          "status": "ok",
          "timestamp": 1569251993245,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": -60
        },
        "id": "l3sAyfNKpKsC",
        "outputId": "27495ee5-27c4-417d-b37a-46ec2aed71ae"
      },
      "outputs": [
        {
          "data": {
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IiDQLaWnpDBo0hL/+9ZGqnSy2bt3MrFnPc/PNt1Xd7quvviArazcAb721gDPO6H/YuQYM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\nvTWWw2b2AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x1d346dff2f90\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "@make_val_and_grad_fn\n",
        "def rosenbrock(x):\n",
        "  return 100 * tf.reduce_sum(tf.square(x[1:] - tf.square(x[:-1]))) + \\\n",
        "      tf.reduce_sum(tf.square(1 - x[:-1]))\n",
        "\n",
        "start = tf.zeros(4, dtype=tf.float64)\n",
        "tolerance_range = []\n",
        "num_iterations = []\n",
        "num_func_calls = []\n",
        "for x in range(15):\n",
        "  tolerance = 10.0**(-x)\n",
        "  result = tff_optimizer.conjugate_gradient_minimize(\n",
        "      rosenbrock, \n",
        "      start, \n",
        "      max_iterations=1000, \n",
        "      tolerance=tolerance)\n",
        "  tolerance_range.append(tolerance)\n",
        "  num_iterations.append(result.num_iterations.numpy())\n",
        "  num_func_calls.append(result.num_objective_evaluations.numpy())\n",
        "\n",
        "plt.plot(tolerance_range, num_iterations, label='Iterations')\n",
        "plt.plot(tolerance_range, num_func_calls, label='Objectrive evaluations')\n",
        "plt.semilogx()\n",
        "plt.xlim(1, 1e-14)\n",
        "plt.xlabel('Tolerance')\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "jWpeBDP7r8oO"
      },
      "source": [
        "## Adjustable parameters\n",
        "\n",
        "The Conjugate Gradient algorithm has several adjustable parameters. These parameters can be passed using the `params` argument. For details on the parameters refer\n",
        "to the [source code](https://github.com/google/tf-quant-finance/blob/master/tf_quant_finance/math/optimizer/conjugate_gradient.py) and [this article](http://users.clas.ufl.edu/hager/papers/CG/cg_compare.pdf).\n",
        "\n",
        "The example below shows how to adjust custom algorithm parameters. We will vary the parameter $\\sigma$ and see how that affects the number of iterations and the number of objective evaluations needed for convergence."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "height": 520
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 1327,
          "status": "ok",
          "timestamp": 1569251999000,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": -60
        },
        "id": "z0oz6cQtDp2y",
        "outputId": "536e3821-1689-470e-bdce-e4d6d08f18ae"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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ABjrA3DMAADgSARo4DuaeAQDA0UgDwDEw9wwAANpDgAaOgblnAADQHgI00A7m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\nAAAASUVORK5CYII=\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x1d346d6a9bd0\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "@make_val_and_grad_fn\n",
        "def func(x):\n",
        "  return (1 - x[0])**2 + 100*(x[1]-x[0]**2)**2\n",
        "\n",
        "start = tf.zeros(2, dtype=tf.float64)\n",
        "delta_range = np.linspace(0.05, 0.5, 9) \n",
        "num_iterations = []\n",
        "num_func_calls = []\n",
        "for delta in delta_range:\n",
        "  result = tff_optimizer.conjugate_gradient_minimize(\n",
        "      func, \n",
        "      start, \n",
        "      max_iterations=1000,\n",
        "      params = tff_optimizer.ConjugateGradientParams(\n",
        "          sufficient_decrease_param=delta))\n",
        "  num_iterations.append(result.num_iterations.numpy())\n",
        "  num_func_calls.append(result.num_objective_evaluations.numpy())\n",
        "  \n",
        "plt.plot(delta_range, num_iterations, label='Iterations')\n",
        "plt.plot(delta_range, num_func_calls, label='Objectrive evaluations')\n",
        "plt.xlabel(r'$\\delta$')\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "Uz1gsJ0wAfoN"
      },
      "source": [
        "## Batching\n",
        "\n",
        "Batching is a powerful feature of TensorFlow. It is an ability to perform the same operations with different components of tensors in parallel. Optimization algorithms in TensorFlow Finance are designed to support batching (although batches can only be 1-dimensional).\n",
        "\n",
        "There are two use cases when batches may be useful:\n",
        "\n",
        "* You have one function, but want to try optimizing it starting from different initial positions.\n",
        "\n",
        "* You have a parametrized family of functions, and you want to optimize all of them in parallel."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "p-digpv8Dqqz"
      },
      "source": [
        "## Batching example: one function, many starting points."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "eZ0JrKeTDqN9"
      },
      "source": [
        "Assume you have a function with several local minima and you want to find all of them.\n",
        "\n",
        "One way to do so is to perform optimization several times, starting from different inital positions. With batching you can invoke optimization only once, with batch of different inital positions. For this you will have to specify objective function in such a way so it supports batching.\n",
        "\n",
        "For example let's consider [Himmelblau's function](https://en.wikipedia.org/wiki/Himmelblau%27s_function). It has 4 local minima. Let's start optimizing from 30 different random points and plot optimization paths for each of these points.\n",
        "\n",
        "For demonstration, to get intermediary position on each iteration, we will invoke algorithm with different values of `max_iter`. On practice you will have to only invoke it once with `max_iter` sufficiently big for all paths to converge. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "height": 516
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 3153,
          "status": "ok",
          "timestamp": 1569252004476,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": -60
        },
        "id": "2HiyNA27Dp5l",
        "outputId": "17b39c02-2229-4f27-f5c6-fe2c6f7fb5a0"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "All converged after 22 iterations\n"
          ]
        },
        {
          "data": {
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XyHJ6+ofKzpXc9aoAmU+nq7/PveCrqVmFf+VCfSoX24+yqgjsZejzuFTw8/WteJxqmEtf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\nvxr0v28bR7/6C6b2vE7bZb0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J0ltOF1JKOmGT2JsHSFzSSeSFIaK/GiZ8aJzYNb1YAxHM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T8W52MrWSJx7pakzHk8uxRRJnMpIlme7meZOraSFxJhxUzK6Y7Dluda9yWl/V3MuNFSRH/913/N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\n7dYb0FMtczRjtfE+65pEdHQpI5cXLOYMXj8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F0IP6lZeT8GjxgHrD86ms9bMMnEsIm9mY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\n5wFLc5EAAAAASUVORK5CYII=\n",
            "text/plain": [
              "\u003cmatplotlib.figure.Figure at 0x1d346e2e3410\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "def himmelblau_function(x, y):\n",
        "  return (x * x + y - 11) ** 2 + (x + y * y - 7) ** 2\n",
        "\n",
        "@make_val_and_grad_fn\n",
        "def objective(coord):\n",
        "  return himmelblau_function(coord[..., 0], coord[..., 1])\n",
        "\n",
        "np.random.seed(0)\n",
        "starts = tf.constant(np.random.uniform(-5, 5, (30, 2)), dtype='float64')\n",
        "\n",
        "paths = []\n",
        "for iter_count in range(100):\n",
        "  results = tff_optimizer.conjugate_gradient_minimize(\n",
        "      objective, \n",
        "      initial_position=starts,\n",
        "      tolerance=1e-8, \n",
        "      max_iterations=iter_count)\n",
        "  paths.append(results.position.numpy())\n",
        "  if (np.all(results.converged.numpy())):\n",
        "    print('All converged after %d iterations' % iter_count)\n",
        "    break\n",
        "\n",
        "# Show the function.\n",
        "x, y = np.meshgrid(np.arange(-5, 5, 0.05), np.arange(-5, 5, 0.05))\n",
        "z = himmelblau_function(x, y)\n",
        "plt.pcolormesh(x, y, z, cmap='RdYlGn', \n",
        "               norm=colors.SymLogNorm(2),\n",
        "               vmin=np.min(z), vmax=np.max(z))\n",
        "plt.colorbar()\n",
        "\n",
        "# Show the paths.\n",
        "paths = np.array(paths)\n",
        "paths_x = paths[:,:,0].T\n",
        "paths_y = paths[:,:,1].T\n",
        "for i in range(len(starts)):\n",
        "  plt.plot(paths_x[i], paths_y[i], marker = '.')\n",
        "\n",
        "plt.xlim(-5, 5)\n",
        "plt.ylim(-5, 5)\n",
        "plt.show()  "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "hT5LA5SMIp-_"
      },
      "source": [
        "We can see, that any path converges to one of four minima."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "HWEjMw3cDyc_"
      },
      "source": [
        "## Batching example: stopping condition\n",
        "\n",
        "Sometimes you might want to find any local minimum, but start from multiple starting points. In this case it's not necessary to wait until all paths converge.\n",
        "\n",
        "Conjugate Gradient algorithm supports parameter `stopping_condition` which specify when to stop optimization. It is a function which takes two boolean tensors, one indicating which optimization paths converged and other - which failed. By default optimization will terminate when all paths converged or failed.\n",
        "\n",
        "However, if you pass `tff_optimizer.converged_any`, algorithm will terminate if at least one path converged (or all failed)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "height": 85
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 167,
          "status": "ok",
          "timestamp": 1569252005029,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": -60
        },
        "id": "4FpDx9HsI0Yp",
        "outputId": "c15516e5-bc9c-499d-c905-470b329700a4"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Converged after 7 iterations.\n",
            "Found minima: [[-2.80511809  3.13131252]\n",
            " [-2.80511809  3.13131252]\n",
            " [-3.77931025 -3.28318599]]\n"
          ]
        }
      ],
      "source": [
        "results = tff_optimizer.conjugate_gradient_minimize(\n",
        "    objective, \n",
        "    initial_position=starts,\n",
        "    tolerance=1e-8,\n",
        "    stopping_condition=tff_optimizer.converged_any)\n",
        "\n",
        "assert np.any(results.converged.numpy())\n",
        "print('Converged after %d iterations.' % results.num_iterations)\n",
        "found_minima = tf.boolean_mask(results.position, results.converged).numpy()\n",
        "print('Found minima: %s' % found_minima)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "gCmPfWW2Oz8Z"
      },
      "source": [
        "You can see that to converge from all points took 22 iterations, but to converge from any point took only 7 iterations, and we found 2 of 4 minima.\n",
        "\n",
        "In the same way you can specify `stopping_condition` for BFGS and L-BFGS algorithms."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "1Oa2P3HvjHEz"
      },
      "source": [
        "## Batching example: multiple functions.\n",
        "\n",
        "Let's consider a simple family of $n$ quadratic functions: \n",
        "$f_i(\\mathbf{x}) = \\|\\mathbf{x} - \\mathbf{a}_i\\|^2_2$. Obviously, minimum of $f_i$ is at the point $\\mathbf{a}_i$. Example below shows how to optimize all such functions simultaneously.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "BrE6YtQLS02R"
      },
      "outputs": [],
      "source": [
        "np.random.seed(12345)\n",
        "dim = 100  # Dimensionality of domain.\n",
        "n = 500    # Number of functions.\n",
        "a = np.random.randn(n, dim)\n",
        "\n",
        "@make_val_and_grad_fn\n",
        "def quadratic(x):\n",
        "  return tf.reduce_sum((x - a) ** 2, axis=-1)\n",
        "\n",
        "results = tff_optimizer.conjugate_gradient_minimize(\n",
        "      quadratic, \n",
        "      initial_position=tf.zeros((n, dim), dtype=tf.float64),\n",
        "      max_iterations=200)\n",
        "\n",
        "assert np.allclose(results.position.numpy() - a, 1e-8)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "V37rc3MNXTTM"
      },
      "source": [
        "## Algorithms overview\n",
        "\n",
        "Code above demonstrates how to use Conjugate Gradient algorithm. TensorFlow Finance provides also implementations of others optimization algorithms:\n",
        "\n",
        "* **[Conjugate Gradient method](https://en.wikipedia.org/wiki/Nonlinear_conjugate_gradient_method)**. This is a first-order method.\n",
        "\n",
        "* **[BFGS](https://en.wikipedia.org/wiki/Broyden%E2%80%93Fletcher%E2%80%93Goldfarb%E2%80%93Shanno_algorithm)**. This is Quasi-Newton first-order method. It needs $O(N^2)$ memory ($N$ - domain dimensionality) to approximate the Hessian matrix, so it may not work for large $N$.\n",
        "\n",
        "* **[L-BFGS](https://en.wikipedia.org/wiki/Limited-memory_BFGS)**. This is optimized version of BFGS which uses less memory.\n",
        "\n",
        "* **[Nelder-Mead](https://en.wikipedia.org/wiki/Nelder–Mead_method)**. This is gradient free method, i.e. it doesn't need gradient. It can be used to optimize non-differentiable function (or a function for which gradient can't be easily computed), but it typically will perform many more evaluations of the objective function than first-order methods.\n",
        "\n",
        "Example below optimizes the same function with all available algorithms."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "colab": {
          "height": 85
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 3289,
          "status": "ok",
          "timestamp": 1569252018629,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": -60
        },
        "id": "frJfc-ReXgbU",
        "outputId": "a008e397-b682-45b5-b4f2-7555a8b377e4"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Objective evaluations with Conjugate Gradient: 297\n",
            "Objective evaluations with BFGS: 124\n",
            "Objective evaluations with L-BFGS: 107\n",
            "Objective evaluations with Nelder-Mead: 1493\n"
          ]
        }
      ],
      "source": [
        "def rosenbrock(x):\n",
        "  return 100 * tf.reduce_sum(tf.square(x[1:] - tf.square(x[:-1]))) + \\\n",
        "      tf.reduce_sum(tf.square(1 - x[:-1]))\n",
        "rosenbrock_with_gradient = make_val_and_grad_fn(rosenbrock)\n",
        "start = tf.zeros(7, dtype=tf.float64)\n",
        "\n",
        "# Conjugate Gradient.\n",
        "result = tff_optimizer.conjugate_gradient_minimize(\n",
        "    rosenbrock_with_gradient,\n",
        "    start,\n",
        "    tolerance=1e-4,\n",
        "    max_iterations=1000)\n",
        "assert(np.allclose(result.position.numpy(), np.ones(7), 1e-4))\n",
        "print(\"Objective evaluations with Conjugate Gradient: %d\" % \n",
        "      result.num_objective_evaluations.numpy())\n",
        "\n",
        "\n",
        "# BFGS.\n",
        "result = tff_optimizer.bfgs_minimize(\n",
        "    rosenbrock_with_gradient,\n",
        "    start,\n",
        "    tolerance=1e-4,\n",
        "    max_iterations=1000)\n",
        "assert(np.allclose(result.position.numpy(), np.ones(7), 1e-4))\n",
        "print(\"Objective evaluations with BFGS: %d\" % \n",
        "      result.num_objective_evaluations.numpy())\n",
        "\n",
        "# L-BFGS.\n",
        "result = tff_optimizer.lbfgs_minimize(\n",
        "    rosenbrock_with_gradient, \n",
        "    start,\n",
        "    tolerance=1e-4,\n",
        "    max_iterations=1000)\n",
        "assert(np.allclose(result.position.numpy(), np.ones(7), 1e-4))\n",
        "print(\"Objective evaluations with L-BFGS: %d\" % \n",
        "      result.num_objective_evaluations.numpy())\n",
        "\n",
        "# Nelder-Mead.\n",
        "result = tff_optimizer.nelder_mead_minimize(\n",
        "    rosenbrock, \n",
        "    initial_vertex=start,\n",
        "    position_tolerance=1e-4,\n",
        "    max_iterations=1000)\n",
        "assert(np.allclose(result.position.numpy(), np.ones(7), 1e-4))\n",
        "print(\"Objective evaluations with Nelder-Mead: %d\" % \n",
        "      result.num_objective_evaluations.numpy())"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "For more examples on BFGS, L-BFGS and Nelder-Mead methods, refer to [this example](https://github.com/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/Optimizers_in_TensorFlow_Probability.ipynb) from TensorFlow Probability."
      ]
    }
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